Question 1

round(pnorm(979,1300,sqrt(40000),lower.tail=FALSE), 4)
## [1] 0.9458

The probability that a randomly selected steer weighs greater than 979lbs is appoximately 94.56%.

Question 2

round(pnorm(8340,11000,sqrt(1960000), lower.tail=FALSE),4)
## [1] 0.9713

The probability that an SVGA monitor’s life span is greater than 8340 hours is appoximately 97.13%.

Question 3

round(pnorm(85,80,3) - pnorm(83,80,3),4)
## [1] 0.1109

The probability that a randomly selected firm earns between 83 and 85 million dollars is approximately 11.09%.

Question 4

round(qnorm(.14,456,123,lower.tail=FALSE))
## [1] 589

The minimum score required for the job offer is 589.

Question 5

round(qnorm(.07,6.13,0.06),2)
## [1] 6.04
round(qnorm(.07,6.13,0.06, lower.tail=FALSE),2)
## [1] 6.22

Nail below 6.04cm and above 6.22cm should be rejected.

Question 6

round(qnorm(.45,78.8,9.8,lower.tail=FALSE))
## [1] 80
round(qnorm(.20,78.8,9.8))
## [1] 71

The range of values for a C grade at 71 to 80.

Question 7

round(qnorm(.45,21.2,5.4,lower.tail=FALSE),2)
## [1] 21.88

The minimum score required for admission is 21.88.

Question 8

round(pbinom(10,151,.09),4)
## [1] 0.192

The probaiblity that less than 11 out of 151 will not graduate on time is appoximately 19.2%.

Question 9

round(pnorm(48.83,48,48/sqrt(147),lower.tail=FALSE),4)
## [1] 0.417

The probabliity that the mean of the sample is greater than 48.83 months is appoximately 41.7%.

Question 10

round(pnorm(93.54,91,10/sqrt(68),lower.tail=FALSE),4)
## [1] 0.0181

The probaiblity that a sample of computers would have a mean life greater than 93.54 months is appoximately 1.81%.

Question 11

round(diff(pbinom(c(21.6,54),540,.07)),4)
## [1] 0.9947

The probability of being within 3% of the mean is approximately 99.47%.

Question 12

round(1-diff(pbinom(c(114.38,162.54),602,.23)),4)
## [1] 0.02

The probability of being outside of 4% of the mean is appoximately 2%.

Question 13

CI <- qnorm(.90)*.8/sqrt(208)
sprintf('(%s,%s)',round(3.9-CI,1),round(3.9+CI,1))
## [1] "(3.8,4)"

It can be stated with 80% confidence that the mean amount of beef eating per week amongst males over 48 is between 3.8 and 4lbs.

Question 14

CI <- qnorm(.99)*11/sqrt(7472)
sprintf('(%s,%s)',round(16.6-CI,1),round(16.6+CI,1))
## [1] "(16.3,16.9)"

It can be stated with 98% confidence that the mean per capite income is between 16.3 and 16.9 thousand dollars.

Question 15

qnorm(.05)
## [1] -1.644854

Upper Left Corner The t value is -1.644.

Question 16

a

values <- c(383.6, 347.1, 371.9, 347.6, 325.8, 337)
m <- mean(values)

b

sd <- sd(values)

c

CV <- qnorm(.95)

d

CI <- CV*sd/sqrt(length(values))
sprintf('(%s,%s)',round(m-CI,1),round(m+CI,1))
## [1] "(337.6,366.7)"

It can be stated with 90% confidence that the mean level of helium gase present in the facility is between 337.6 and 366.7 picocuries per liter.

Question 17

a

CV <- round(qnorm(.90),3)

b

CI <- CV*2.45/sqrt(16)
sprintf('(%s,%s)',round(46.4-CI,1),round(46.4+CI,1))
## [1] "(45.6,47.2)"

It can be stated with 80% confidence that the mean amoutn of bushels per acre is between 45.6 and 47.2.

Question 18

ceiling((qnorm(.995)*1.9/.13)^2)
## [1] 1418

A sample of 1418 is required.

Question 19

ceiling((qnorm(.975)*sqrt(3.61)/.19)^2)
## [1] 385

A sample of 385 is required.

Question 20

a

m <- (2089-1734)/2089
round(m, 3)
## [1] 0.17

b

CI <- qnorm(.99)*sqrt(m*(1-m)/2089)
sprintf('(%s,%s)',round(m-CI,3),round(m+CI,3))
## [1] "(0.151,0.189)"

It can be stated with 98% confidence that the proportion of 10th graders that can read above an 8th grade level is between 15.1% and 18.9%.

Question 21

a

m <- 156/474
round(m,3)
## [1] 0.329

b

CI <- qnorm(.975)*sqrt(m*(1-m)/474)
sprintf('(%s,%s)',round(m-CI,3),round(m+CI,3))
## [1] "(0.287,0.371)"

It can be stated with 95% confidence that the proportion of oil tankers that have a spill is between 28.7% and 37.1%.